Problem Statement

Create a program that, when run, would display all integers from   1   to   ∞   (or any relevant implementation limit),   in sequence   (i.e.   1, 2, 3, 4, etc)   if given enough time.

An example may not be able to reach arbitrarily-large numbers based on implementations limits.   For example, if integers are represented as a 32-bit unsigned value with 0 as the smallest representable value, the largest representable value would be 4,294,967,295.   Some languages support arbitrarily-large numbers as a built-in feature, while others make use of a module or library. If appropriate, provide an example which reflect the language implementation's common built-in limits as well as an example which supports arbitrarily large numbers, and describe the nature of such limitations—or lack thereof.

Let's start with the solution:

/* NetRexx */
options replace format comments java crossref symbols binary

k_ = Rexx
bigDigits = 999999999 -- Maximum setting for digits allowed by NetRexx
numeric digits bigDigits

loop k_ = 1
  say k_
  end k_

/* NetRexx */
options replace format comments java crossref symbols binary

import java.math.BigInteger

-- allow an option to change the output radix.
parse arg radix .
if radix.length() == 0 then radix = 10 -- default to decimal
k_ = BigInteger
k_ = BigInteger.ZERO

loop forever
  k_ = k_.add(BigInteger.ONE)
  say k_.toString(int radix)
  end